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Answer:

43 1 ÷12

Step-by-step explanation:

The computation of the length of the original roll of papers is shown below:

36 1 ÷3 and 6 3 ÷ 4 together

Now convert the above fractions into a number

36 1 ÷ 3 = 109 ÷3

And,

6 3 ÷4 = 27 ÷ 4

Now add these two numbers i.e.

109 ÷3  + 27 ÷ 4

= 436 + 81 ÷ 12

= 517 ÷12

= 43 1 ÷12

Given:

The graph of an inequality.

To find:

The point which is a solution of the given graph of inequality.

Solution:

From the given graph it is clear that the boundary line of the graph is a dotted line. It means the points lie in shaded region are in the solution set but the points on the line are not included in the solution set.

The points (3,2) and (-3,-6) are lie on the boundary line. it means they are not the solution of the inequality represented by the given graph.

Point (5,0) lies on the positive x-axis at the distance of 5 units from the origin and it doesn't lies in the shaded region. So, (5,0) is not a solution.

Point (0,5) lies on the negative y-axis at the distance of 5 units from the origin and it lies in the shaded region. So, (0,5) is a solution.

Therefore, the correct option is B.

Answer:

2

Step-by-step explanation:

first use order of operations.

1/2(4^2)-6

1/2*16-6

then simplify to get:

8-6=2

Answer: 2

Step-by-step explanation:

The question is asking you to substitute the b with 4 and find the solution to the expression.

[tex]\frac{1}{2}b^{2} -6[/tex]

[tex]=\frac{1}{2}(4)^{2} -6[/tex]

[tex]=\frac{1}{2}(16) -6[/tex] (PEMDAS so you do the exponent first)

[tex]=8 -6[/tex] (PEMDAS so you do the multiplication first)

[tex]=2[/tex]

Answer:

w=10 cm

Step-by-step explanation:

The formula for the volume of a rectangular prism is V=whl.

So in this case, the equation would be 1560=w·12·(w+3). Then, we can simplify this equation.

1. Divide 12 to both sides of the equation. 1560/12=130. The equation becomes 130=w(w+3).

2. Distribute w through the parentheses, the equation becomes 130=w²+3w.

3. Then, -130 from both sides of the equation, so we can get the quadratic: w²+3w-130=0.

4. Factor the quadratic. w²+3w-130=(w-10)(w+13).

5. (w-10)(w+13)=0. w=10 or w=-13. However, w is the width of a rectangular prism, can the width of a shape be negative? No. So we can ignore the solution w=-13. Therefore, w=10cm.

6. To make sure our answer is correct, let's substitute the values back into the volume of a rectangular prism formula: V=whl. w=10; h=12; l=10+3=13; V=10(12)(13)=120*13=1560 cm³. As a result, our answer is correct, w=10 cm.

Hope this helps, have a nice day.

Answer:

5

Step-by-step explanation:

13² - 12² = 25

√25 = 5

Have a great day <3

Answer:

The chlorine tablets are $36 and the pH test kit is $4.40.

Step-by-step explanation:

So what I first did was add 90+11 (because $90 for the chlorine tablets and $11 for the pH kit). The answer you should get is 101.  From their I did 101 multiplied by 40% or 101 multiplied by .40 (40% and 0.40 are the same thing). You now get $40.4.  

Now I did 90·40%. I got $36

Then I did 11·40%. I got 4.4

I added them up and got $40.4 which was my new price so now we know that the chlorine tablets are $36 and the pH test kit is $4.40.

Answer:

x = -1

Step by step explanation:

Distribute 6

6x-12= -18

Add 12 to both sides

6x= -6

Divide both sides by 6

x= -1

Hope this helps

The integrat (cos(x - 3) dx is transformed into L' (t)dt an g(t) = 1/2 sin(t-3/2) is incorrect. The correct option g(t) = 1/2 cos(t-3/2).

To transform the integral ∫cos(x - 3)dx into L'(t)dt using an appropriate change of variable, the substitution method make the substitution:

t = x - 3

To find dt, differentiate both sides of the equation with respect to x:

dt = dx

substitute these expressions into the integral:

∫cos(x - 3)dx = ∫cos(t)dt

The integral has been transformed into ∫cos(t)dt.

regarding the options for g(t),

Option 1: g(t) = 1/2 cos(t-3/2)

Taking the derivative of g(t) with respect to t,

g'(t) = -(1/2)sin(t - 3/2)

Option 2: g(t) = 1/2 sin(t-3/2)

Taking the derivative of g(t) with respect to t,

g'(t) = (1/2)cos(t - 3/2)

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Answer:

P = 528

Step-by-step explanation:

P = a + b + c = 200 + 107 + 221 = 528

Answer:

the shape isnt angled thats what it means

Step-by-step explanation:

Answer:

77.28

Step-by-step explanation:

c=π2r

12.3 times 2 =

24.6π

=77.28317928

=77.28

Answer:

77.3

Step-by-step explanation:

The exact values  of sin x, tan x and sec x in simplest form are: sin x = -√3/2, tan x = √3, sec x = -2/√3.

To solve this problem, we'll work with the angle x, which is equal to -14π/3. Part a: Determine the reference angle of x. The reference angle is the positive acute angle formed between the terminal side of the angle and the x-axis. To find the reference angle, we ignore the negative sign and convert the angle to its equivalent positive angle within one revolution.

The positive equivalent angle can be obtained by adding 2π (or 360 degrees) repeatedly until we obtain a positive angle. In this case, we have: -14π/3 + 2π = -14π/3 + 6π/3 = -8π/3. The reference angle of x is 8π/3. Part b: Find the exact values of sin x, tan x, and sec x in simplest form. sin x = sin(-14π/3) = -sin(14π/3) (Using the symmetry of sine function)

= -sin(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)

= -sin(2π/3) (Sine of an angle 2π/3 is known) = -√3/2.

tan x = tan(-14π/3) = tan(14π/3) (Using the symmetry of tangent function)

= tan(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)

= tan(2π/3) (Tangent of an angle 2π/3 is known)= √3. sec x = sec(-14π/3) = sec(14π/3) (Using the symmetry of secant function)= sec(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)= sec(2π/3) (Secant of an angle 2π/3 is known)= -2/√3. Therefore, the exact values in simplest form are: sin x = -√3/2, tan x = √3, sec x = -2/√3.

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Answer: The exact values  of sin x, tan x and sec x in simplest form are: sin x = -√3/2, tan x = √3, sec x = -2/√3.

Step-by-step explanation: To solve this problem, we'll work with the angle x, which is equal to -14π/3. Part a: Determine the reference angle of x. The reference angle is the positive acute angle formed between the terminal side of the angle and the x-axis. To find the reference angle, we ignore the negative sign and convert the angle to its equivalent positive angle within one revolution.

The positive equivalent angle can be obtained by adding 2π (or 360 degrees) repeatedly until we obtain a positive angle. In this case, we have: -14π/3 + 2π = -14π/3 + 6π/3 = -8π/3. The reference angle of x is 8π/3. Part b: Find the exact values of sin x, tan x, and sec x in simplest form. sin x = sin(-14π/3) = -sin(14π/3) (Using the symmetry of sine function)

= -sin(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)

= -sin(2π/3) (Sine of an angle 2π/3 is known) = -√3/2.

tan x = tan(-14π/3) = tan(14π/3) (Using the symmetry of tangent function)

= tan(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)

= tan(2π/3) (Tangent of an angle 2π/3 is known)= √3. sec x = sec(-14π/3) = sec(14π/3) (Using the symmetry of secant function)= sec(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)= sec(2π/3) (Secant of an angle 2π/3 is known)= -2/√3. Therefore, the exact values in simplest form are: sin x = -√3/2, tan x = √3, sec x = -2/√3.

The renewal-type equation for E[SN(1)+1] is E[SN(1)+1] = 2, indicating that the expected value of the sum of the number of renewals by time 1 plus 1 is equal to 2.

To derive a renewal-type equation for E[SN(1)+1], we can use the renewal-reward theorem.

Let Tn be the interarrival times of the renewal process, where n represents the nth renewal. The random variable N(t) represents the number of renewals that occur by time t.

Using the renewal-reward theorem, we have:

E[SN(1)+1] = E[T1 + T2 + ... + TN(1) + 1]

Since the interarrival times are independent and identically distributed (i.i.d.), we can express this as:

E[SN(1)+1] = E[T] * E[N(1)] + 1

Now, we need to compute the expressions for E[T] and E[N(1)].

E[T] represents the expected interarrival time, which is equal to the reciprocal of the renewal rate. Let λ be the renewal rate, then E[T] = 1/λ.

E[N(1)] represents the expected number of renewals by time 1. This can be calculated using the renewal equation:

E[N(t)] = λ * t

Therefore, E[N(1)] = λ * 1 = λ.

Substituting these expressions back into the renewal-type equation, we have:

E[SN(1)+1] = (1/λ) * λ + 1 = 1 + 1 = 2

Hence, the renewal-type equation for E[SN(1)+1] is E[SN(1)+1] = 2.

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Median = 87.5 Sorry about the other one

To close the $2,000 in expenses, $5,000 in revenue, and $500 in dividends, we need to transfer these amounts to the appropriate accounts and close the temporary accounts at the end of the accounting period. Here are the journal entries to close these amounts:

Close Expenses:

Date | Account | Debit | Credit

End of Year | Expenses | $2,000 |

| Income Summary | | $2,000

Close Revenue:

Date | Account | Debit | Credit

End of Year | Income Summary | $5,000 |

| Revenue | | $5,000

Close Dividends:

Date | Account | Debit | Credit

End of Year | Retained Earnings | $500 |

| Dividends | | $500

After these closing entries, the balances of the temporary accounts (Expenses, Revenue, and Dividends) will be zero, and their respective amounts will be transferred to the Income Summary and Retained Earnings accounts. The Income Summary account will show the net income (revenue minus expenses) for the period.

Please note that the specific account titles may vary depending on the company's chart of accounts, so make sure to use the appropriate account titles according to your specific chart of accounts.

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The proportion of adults with scores above 110 is 0.1841.

Here, we have,

It should be noted that from the information illustrated, Wechsler Adult Intelligence Scale scores are approximately Normal, with a mean of 100 and a standard deviation of 11.

The formula to use will be:

P(a < Z < b) = P(Z < b) – P(Z < a)

a = lower value

b = higher value

Z = z value

It should be noted that the proportion of adults with scores above 110 will be:

= P(x > 110)

= P(z > 110 - 100/11)

= P(z > 0.90)

= 1 - 0.8159

= 0.1841

Therefore, this illustrates those that has scores of more than 110.

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Answer:

( 6, -1 )

Step-by-step explanation:

When you rotate 1 from the x axis by 90° it becomes -1 from the y axis.

When you rotate 6 by 9° from thr y axis, it becomes again 6 on the x axis

Your new x value is 6 and y is -1

So (6,-1)

Answer:

(-6, 1)

Step-by-step explanation:

To find the point obtained by rotating point P = (1, 6) counterclockwise by an angle of 90 degrees (r₉₀°), we can use the rotation formula:

x' = x * cos(θ) - y * sin(θ)

y' = x * sin(θ) + y * cos(θ)

In this case, θ is 90 degrees.

Substituting the values into the formula:

x' = 1 * cos(90°) - 6 * sin(90°)

y' = 1 * sin(90°) + 6 * cos(90°)

cos(90°) = 0 and sin(90°) = 1, so we have:

x' = 1 * 0 - 6 * 1 = -6

y' = 1 * 1 + 6 * 0 = 1

Therefore, r₉₀°(P) = (-6, 1). The point P = (1, 6) rotates counterclockwise by 90 degrees to the point (-6, 1).

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Width of Heng's area model is  2x + 1

Step-by-step explanation:

Given:

Greatest common factor is 5x

To Find:

The width = ?

Solution:

let the  be the area

And  5x be the length

Then area  = length  x  width

Now rewriting the formula for width, we get

Width =  

Substituting the values in the above formula

Width =

Width = 2x + 1

Answer: the answer is b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

first add them together. the y cancels out and your left with 3x=15. divide by 3 on both sides and you get x=5. The only answer with positive 5 as an x value is b

The area of the sector with a central angle of 27/8 radians in a circle of radius 4 meters is 27 square meters.

To find the area of a sector, you can use the formula:

Area of Sector = (θ/2π) * πr²

where θ is the central angle in radians and r is the radius of the circle.

Given:

Central angle (θ) = 27/8 radians

Radius (r) = 4 meters

Substituting the given values into the formula, we have:

Area of Sector = (27/8 * 1/(2π)) * π * (4)^2

Simplifying the expression:

Area of Sector = (27/8 * 1/2) * (4)^2

Area of Sector = (27/16) * 16

Area of Sector = 27 square meters

Therefore, the area of the sector with a central angle of 27/8 radians in a circle of radius 4 meters is 27 square meters.

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Answer:5.4

Step-by-step explanation:

The function f(x) = 3x²/3 - 2x has no intercepts, a relative minimum at (1, -1), no points of inflection, and no asymptotes.

Intercepts: To find the x-intercepts, we set f(x) equal to zero and solve for x:

0 = 3x²/3 - 2x

0 = x² - 2x

0 = x(x - 2)

x = 0 or x = 2

Therefore, both x = 0 and x = 2 are not actual x-intercepts, but rather double roots.

Relative Extrema: To find the relative extrema, we take the derivative of f(x) and set it equal to zero,

f'(x) = 2x - 2

0 = 2x - 2

2 = 2x

x = 1

Substituting x = 1 back into the original function, we find f(1) = -1. Therefore, the relative minimum occurs at (1, -1).

f''(x) = 2

Since the second derivative is a constant, it never equals zero. Therefore, there are no points of inflection for this function.

Asymptotes: To determine if there are any asymptotes, we examine the behavior of the function as x approaches positive or negative infinity. Since the highest power of x in the function is 2, the graph does not approach any vertical asymptotes.

For horizontal asymptotes, we look at the limits as x approaches positive or negative infinity:

lim(x→∞) f(x) = lim(x→∞) (3x²/3 - 2x) = ∞

The limits approach positive infinity in both cases, indicating that there are no horizontal asymptotes. Graphically, the function represents a parabola that opens upwards, with a relative minimum at (1, -1).

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Answer: 95

Step-by-step explanation:

Think of 1/8 times 760 as 760/8 because it’s the same thing.

Answer:F : 13 1/2

Step-by-step explanation:27 divided by 2 is 13 1/2

The linear trendline used to forecast sales for a given time period takes the form y = b0 + b1t, where y represents the estimated sales, b0 is the constant term, b1 is the coefficient of the time period variable (t), and t is the time period.

In this equation, the coefficient b1 determines the relationship between the time period and the estimated sales. If b1 increases, it means that for each additional time period, the estimated sales will also increase. On the other hand, if b1 is constant, it implies that the estimated sales do not change with each additional time period.

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The blue dot located inside the curve of the parabola is Focus.

What are Parts in Parabola?

The essential feature of a parabola is that all of its points are the same distance from a point called the focus and a line called the directrix. The vertex, axis, latus rectum, and focal length are also key components of a parabola.

The latus rectum, also known as the focal diameter, is the line segment that runs through the focus and parallel to the directrix. The focal diameter's endpoints are located on the curve.

A parabola is the set of all points ( x, y ) in a plane that are the same distance from a fixed line called the directrix and a fixed point not on the directrix (the focus).

A parabola will have three key components: a focus, a directrix, and a vertex. This upward-opening parabola demonstrates that all points,, along the parabola's curve will be the same distance from the focus and the directrix.

Thus, the blue dot located inside the curve of the parabola is Focus.

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The work of providing air traffic control and radar services in the United States falls under the purview of the Federal Aviation Administration (FAA). ATC and radar services that  cover all airspace over the United States, regardless of whether flights are domestic or international.

FAA provides ATC and radar services in the US. ATC and radar services cover all US airspace, including domestic and international flights. The FAA manages the NAS, covering 29.5 million sq mi. This includes airspace over the entire United States, including Alaska, Hawaii, Guam, Puerto Rico. VI ATC monitors varying number of aircraft based on time, weather, and traffic.

The FAA deals with 44k flights daily in the US. Note that this number may increase during peak travel periods. The FAA manages ATC for 13k+ US airports. Incl. international, regional, gen. aviation & priv. airstrips. The number can vary due to new or old airports.

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Answer:

c y=6x+4

Step-by-step explanation: